Yeast chorismate mutase in the R state: Simulations of the active site

The isomerization of chorismate to prephenate by chorismate mutase in the biosynthetic pathway that forms Tyr and Phe involves C5—O (ether) bond cleavage and C1—C9 bond formation in a Claisen rearrangement. Development of negative charge on the ether oxygen, stabilized by Lys-168 and Glu-246, is inferred from the structure of a complex with a transition state analogue (TSA) and from the pH-rate profile of the enzyme and the E246Q mutant. These studies imply a protonated Glu-246 well above pH 7. Here, several 500-ps molecular dynamics simulations test the stability of enzyme–TSA complexes by using a solvated system with stochastic boundary conditions. The simulated systems are (i) protonated Glu-246 (stable), (ii) deprotonated Glu-246 (unstable), (iii) deprotonated Glu-246 plus one H2O between Glu-246 and the ether oxygen (unstable), (iv) the E246Q mutant (stable), and (v) addition of OH− between protonated Glu-246 and the ether oxygen. In (v), a local conformational change of Lys-168 displaced the OH− into the solvent region, suggesting a possible rate-determining step that precedes the catalytic step. In a 500-ps simulation of the enzyme complexed with the reactant chorismate or the product prephenate, no water molecule remained near the oxygen of the ligand. Calculations using the linearized Poisson–Boltzmann equation show that the effective pKa of Glu-246 is shifted from 5.8 to 8.1 as the negative charge on the ether oxygen of the TSA is changed from −0.56 electron to −0.9 electron. Altogether, these results support retention of a proton on Glu-246 to high pH and the absence of a water molecule in the catalytic steps.

A fast, high resolution, second-order central scheme for incompressible flows

A high resolution, second-order central difference method for incompressible flows is presented. The method is based on a recent second-order extension of the classic Lax–Friedrichs scheme introduced for hyperbolic conservation laws (Nessyahu H. & Tadmor E. (1990) J. Comp. Physics. 87, 408-463; Jiang G.-S. & Tadmor E. (1996) UCLA CAM Report 96-36, SIAM J. Sci. Comput., in press) and augmented by a new discrete Hodge projection. The projection is exact, yet the discrete Laplacian operator retains a compact stencil. The scheme is fast, easy to implement, and readily generalizable. Its performance was tested on the standard periodic double shear-layer problem; no spurious vorticity patterns appear when the flow is underresolved. A short discussion of numerical boundary conditions is also given, along with a numerical example.

Rock friction and its implications for earthquake prediction examined via models of Parkfield earthquakes.

The friction of rocks in the laboratory is a function of time, velocity of sliding, and displacement. Although the processes responsible for these dependencies are unknown, constitutive equations have been developed that do a reasonable job of describing the laboratory behavior. These constitutive laws have been used to create a model of earthquakes at Parkfield, CA, by using boundary conditions appropriate for the section of the fault that slips in magnitude 6 earthquakes every 20-30 years. The behavior of this model prior to the earthquakes is investigated to determine whether or not the model earthquakes could be predicted in the real world by using realistic instruments and instrument locations. Premonitory slip does occur in the model, but it is relatively restricted in time and space and detecting it from the surface may be difficult. The magnitude of the strain rate at the earth's surface due to this accelerating slip seems lower than the detectability limit of instruments in the presence of earth noise. Although not specifically modeled, microseismicity related to the accelerating creep and to creep events in the model should be detectable. In fact the logarithm of the moment rate on the hypocentral cell of the fault due to slip increases linearly with minus the logarithm of the time to the earthquake. This could conceivably be used to determine when the earthquake was going to occur. An unresolved question is whether this pattern of accelerating slip could be recognized from the microseismicity, given the discrete nature of seismic events. Nevertheless, the model results suggest that the most likely solution to earthquake prediction is to look for a pattern of acceleration in microseismicity and thereby identify the microearthquakes as foreshocks.

Numerical vorticity creation based on impulse conservation.

The problem of creating solenoidal vortex elements to satisfy no-slip boundary conditions in Lagrangian numerical vortex methods is solved through the use of impulse elements at walls and their subsequent conversion to vortex loops. The algorithm is not uniquely defined, due to the gauge freedom in the definition of impulse; the numerically optimal choice of gauge remains to be determined. Two different choices are discussed, and an application to flow past a sphere is sketched.

Equações de onda generalizadas e quantização funtorial para teorias de campo escalar livre

Nesta dissertação apresentamos um método de quantização matemática e conceitualmente rigoroso para o campo escalar livre de interações. Trazemos de início alguns aspéctos importantes da Teoria de Distribuições e colocamos alguns pontos de geometria Lorentziana. O restante do trabalho é dividido em duas partes: na primeira, estudamos equações de onda em variedades Lorentzianas globalmente hiperbólicas e apresentamos o conceito de soluções fundamentais no contexto de equações locais. Em seguida, progressivamente construímos soluções fundamentais para o operador de onda a partir da distribuição de Riesz. Uma vez estabelecida uma solução para a equação de onda em uma vizinhança de um ponto da variedade, tratamos de construir uma solução global a partir da extensão do problema de Cauchy a toda a variedade, donde as soluções fundamentais dão lugar aos operadores de Green a partir da introdução de uma condição de contorno. Na última parte do trabalho, apresentamos um mínimo da Teoria de Categorias e Funtores para utilizar esse formalismo na contrução de um funtor de segunda quantização entre a categoria de variedades Lorentzianas globalmente hiperbólicas e a categoria de redes de álgebras C* satisfazendo os axiomas de Haag-Kastler. Ao fim, retomamos o caso particular do campo escalar quântico livre.

Método da propagação de feixe de ângulo largo para análise de guias de ondas ópticos não-lineares

Este trabalho propõe uma extensão do método de propagação de feixe (BPM - Beam Propagation Method) para a análise de guias de ondas ópticos e acopladores baseados em materiais não-lineares do tipo Kerr. Este método se destina à investigação de estruturas onde a utilização da equação escalar de Helmholtz (EEH) em seu limite paraxial não mais se aplica. Os métodos desenvolvidos para este fim são denominados na literatura como métodos de propagação de feixe de ângulo largo. O formalismo aqui desenvolvido é baseado na técnica das diferenças finitas e nos esquemas de Crank-Nicholson (CN) e Douglas generalizado (GD). Estes esquemas apresentam como característica o fato de apresentarem um erro de truncamento em relação ao passo de discretização transversal, Δx, proporcional a O(Δx2) para o primeiro e O(Δx4). A convergência do método em ambos esquemas é otimizada pela utilização de um algoritmo interativo para a correção do campo no meio não-linear. O formalismo de ângulo largo é obtido pela expansão da EEH para os esquemas CN e GD em termos de polinômios aproximantes de Padé de ordem (1,0) e (1,1) para CN e GD, e (2,2) e (3,3) para CN. Os aproximantes de ordem superior a (1,1) apresentam sérios problemas de estabilidade. Este problema é eliminado pela rotação dos aproximantes no plano complexo. Duas condições de contorno nos extremos da janela computacional são também investigadas: 1) (TBC - Transparent Boundary Condition) e 2) condição de contorno absorvente (TAB - Transparent Absorbing Boundary). Estas condições de contorno possuem a facilidade de evitar que reflexões indesejáveis sejam transmitidas para dentro da janela computacional. Um estudo comparativo da influência destas condições de contorno na solução de guias de ondas ópticos não-lineares é também abordada neste trabalho.

Avaliação de métodos numéricos de análise linear de estabilidade para perfis de aço formados a frio.

Para o projeto de estruturas com perfis de aço formados a frio, é fundamental a compreensão dos fenômenos da instabilidade local e global, uma vez que estes apresentam alta esbeltez e baixa rigidez à torção. A determinação do carregamento crítico e a identificação do modo de instabilidade contribuem para o entendimento do comportamento dessas estruturas. Este trabalho avalia três metodologias para a análise linear de estabilidade de perfis de aço formados a frio isolados, com o objetivo de determinar os carregamentos críticos elásticos de bifurcação e os modos de instabilidade associados. Estritamente, analisa-se perfis de seção U enrijecido e Z enrijecido isolados, de diversos comprimentos e diferentes condições de vinculação e carregamento. Determinam-se os carregamentos críticos elásticos de bifurcação e os modos de instabilidade globais e locais por meio de: (i) análise com o Método das Faixas Finitas (MFF), através do uso do programa computacional CUFSM; (ii) análise com elementos finitos de barra baseados na Teoria Generalizada de Vigas (MEF-GBT), via uso do programa GBTUL; e (iii) análise com elementos finitos de casca (MEF-cascas) por meio do uso do programa ABAQUS. Algumas restrições e ressalvas com relação ao uso do MFF são apresentadas, assim como limitações da Teoria Generalizada de Viga e precauções a serem tomadas nos modelos de cascas. Analisa-se também a influência do grau de discretização da seção transversal. No entanto, não é feita avaliação em relação aos procedimentos normativos e tampouco análises não lineares, considerando as imperfeições geométricas iniciais, tensões residuais e o comportamento elastoplástico do material.

Modelo computacional para avaliação do desempenho hidrodinâmico de embarcações de planeio em águas calmas.

Em geral, uma embarcação de planeio é projetada para atingir elevados níveis de velocidade. Esse atributo de desempenho está diretamente relacionado ao porte da embarcação e à potência instalada em sua planta propulsiva. Tradicionalmente, durante o projeto de uma embarcação, as análises de desempenho são realizadas através de resultados de embarcações já existentes, retirados de séries sistemáticas ou de embarcações já desenvolvidas pelo estaleiro e/ou projetista. Além disso, a determinação dos atributos de desempenho pode ser feita através de métodos empíricos e/ou estatísticos, onde a embarcação é representada através de seus parâmetros geométricos principais; ou a partir de testes em modelos em escala reduzida ou protótipos. No caso específico de embarcações de planeio, o custo dos testes em escala reduzida é muito elevado em relação ao custo de projeto. Isso faz com que a maioria dos projetistas não opte por ensaios experimentais das novas embarcações em desenvolvimento. Ao longo dos últimos anos, o método de Savitsky foi largamente utilizado para se realizar estimativas de potência instalada de uma embarcação de planeio. Esse método utiliza um conjunto de equações semi-empíricas para determinar os esforços atuantes na embarcação, a partir dos quais é possível determinar a posição de equilíbrio de operação e a força propulsora necessária para navegar em uma dada velocidade. O método de Savitsky é muito utilizado nas fases iniciais de projeto, onde a geometria do casco ainda não foi totalmente definida, pois utiliza apenas as características geométricas principais da embarcação para realização das estimativas de esforços. À medida que se avança nas etapas de projeto, aumenta o detalhamento necessário das estimativas de desempenho. Para a realização, por exemplo, do projeto estrutural é necessária uma estimativa do campo de pressão atuante no fundo do casco, o qual não pode ser determinado pelo método de Savitsky. O método computacional implementado nesta dissertação, tem o objetivo de determinar as características do escoamento e o campo de pressão atuante no casco de uma embarcação de planeio navegando em águas calmas. O escoamento é determinado através de um problema de valor de contorno, no qual a superfície molhada no casco é considerada um corpo esbelto. Devido ao uso da teoria de corpo esbelto o problema pode ser tratado, separadamente, em cada seção, onde as condições de contorno são forçadamente respeitadas através de uma distribuição de vórtices.

On the development of advanced techniques for mixed-elastohydrodynamic lubrification modelling of journal and sliding bearing systems.

The present thesis is focused on the development of a thorough mathematical modelling and computational solution framework aimed at the numerical simulation of journal and sliding bearing systems operating under a wide range of lubrication regimes (mixed, elastohydrodynamic and full film lubrication regimes) and working conditions (static, quasi-static and transient conditions). The fluid flow effects have been considered in terms of the Isothermal Generalized Equation of the Mechanics of the Viscous Thin Films (Reynolds equation), along with the massconserving p-Ø Elrod-Adams cavitation model that accordingly ensures the so-called JFO complementary boundary conditions for fluid film rupture. The variation of the lubricant rheological properties due to the viscous-pressure (Barus and Roelands equations), viscous-shear-thinning (Eyring and Carreau-Yasuda equations) and density-pressure (Dowson-Higginson equation) relationships have also been taken into account in the overall modelling. Generic models have been derived for the aforementioned bearing components in order to enable their applications in general multibody dynamic systems (MDS), and by including the effects of angular misalignments, superficial geometric defects (form/waviness deviations, EHL deformations, etc.) and axial motion. The bearing exibility (conformal EHL) has been incorporated by means of FEM model reduction (or condensation) techniques. The macroscopic in fluence of the mixedlubrication phenomena have been included into the modelling by the stochastic Patir and Cheng average ow model and the Greenwood-Williamson/Greenwood-Tripp formulations for rough contacts. Furthermore, a deterministic mixed-lubrication model with inter-asperity cavitation has also been proposed for full-scale simulations in the microscopic (roughness) level. According to the extensive mathematical modelling background established, three significant contributions have been accomplished. Firstly, a general numerical solution for the Reynolds lubrication equation with the mass-conserving p - Ø cavitation model has been developed based on the hybridtype Element-Based Finite Volume Method (EbFVM). This new solution scheme allows solving lubrication problems with complex geometries to be discretized by unstructured grids. The numerical method was validated in agreement with several example cases from the literature, and further used in numerical experiments to explore its exibility in coping with irregular meshes for reducing the number of nodes required in the solution of textured sliding bearings. Secondly, novel robust partitioned techniques, namely: Fixed Point Gauss-Seidel Method (PGMF), Point Gauss-Seidel Method with Aitken Acceleration (PGMA) and Interface Quasi-Newton Method with Inverse Jacobian from Least-Squares approximation (IQN-ILS), commonly adopted for solving uid-structure interaction problems have been introduced in the context of tribological simulations, particularly for the coupled calculation of dynamic conformal EHL contacts. The performance of such partitioned methods was evaluated according to simulations of dynamically loaded connecting-rod big-end bearings of both heavy-duty and high-speed engines. Finally, the proposed deterministic mixed-lubrication modelling was applied to investigate the in fluence of the cylinder liner wear after a 100h dynamometer engine test on the hydrodynamic pressure generation and friction of Twin-Land Oil Control Rings.

Finite Element Analysis of Thermal Buckling in Auotmotive Clutch and Brake Discs

Thermal buckling behavior of automotive clutch and brake discs is studied by making the use of finite element method. It is found that the temperature distribution along the radius and the thickness affects the critical buckling load considerably. The results indicate that a monotonic temperature profile leads to a coning mode with the highest temperature located at the inner radius. Whereas a temperature profile with the maximum temperature located in the middle leads to a dominant non-axisymmetric buckling mode, which results in a much higher buckling temperature. A periodic variation of temperature cannot lead to buckling. The temperature along the thickness can be simplified by the mean temperature method in the single material model. The thermal buckling analysis of friction discs with friction material layer, cone angle geometry and fixed teeth boundary conditions are also studied in detail. The angular geometry and the fixed teeth can improve the buckling temperature significantly. Young’s Modulus has no effect when single material is applied in the free or restricted conditions. Several equations are derived to validate the result. Young’s modulus ratio is a useful factor when the clutch has several material layers. The research findings from this paper are useful for automotive clutch and brake discs design against structural instability induced by thermal buckling.

Dynamical Equations For The Period Vectors In A Periodic System Under Constant External Stress

The purpose of this paper is to derive the dynamical equations for the period vectors of a periodic system under constant external stress. The explicit starting point is Newton’s second law applied to halves of the system. Later statistics over indistinguishable translated states and forces associated with transport of momentum are applied to the resulting dynamical equations. In the final expressions, the period vectors are driven by the imbalance between internal and external stresses. The internal stress is shown to have both full interaction and kinetic-energy terms.

Tight-Binding Approximations in 1D and 2D Coupled-Cavity Photonic Crystal Structures

Light confinement and controlling an optical field has numerous applications in the field of telecommunications for optical signals processing. When the wavelength of the electromagnetic field is on the order of the period of a photonic microstructure, the field undergoes reflection, refraction, and coherent scattering. This produces photonic bandgaps, forbidden frequency regions or spectral stop bands where light cannot exist. Dielectric perturbations that break the perfect periodicity of these structures produce what is analogous to an impurity state in the bandgap of a semiconductor. The defect modes that exist at discrete frequencies within the photonic bandgap are spatially localized about the cavity-defects in the photonic crystal. In this thesis the properties of two tight-binding approximations (TBAs) are investigated in one-dimensional and two-dimensional coupled-cavity photonic crystal structures We require an efficient and simple approach that ensures the continuity of the electromagnetic field across dielectric interfaces in complex structures. In this thesis we develop \textrm{E} -- and \textrm{D} --TBAs to calculate the modes in finite 1D and 2D two-defect coupled-cavity photonic crystal structures. In the \textrm{E} -- and \textrm{D} --TBAs we expand the coupled-cavity \overrightarrow{E} --modes in terms of the individual \overrightarrow{E} -- and \overrightarrow{D} --modes, respectively. We investigate the dependence of the defect modes, their frequencies and quality factors on the relative placement of the defects in the photonic crystal structures. We then elucidate the differences between the two TBA formulations, and describe the conditions under which these formulations may be more robust when encountering a dielectric perturbation. Our 1D analysis showed that the 1D modes were sensitive to the structure geometry. The antisymmetric \textrm{D} mode amplitudes show that the \textrm{D} --TBA did not capture the correct (tangential \overrightarrow{E} --field) boundary conditions. However, the \textrm{D} --TBA did not yield significantly poorer results compared to the \textrm{E} --TBA. Our 2D analysis reveals that the \textrm{E} -- and \textrm{D} --TBAs produced nearly identical mode profiles for every structure. Plots of the relative difference between the \textrm{E} and \textrm{D} mode amplitudes show that the \textrm{D} --TBA did capture the correct (normal \overrightarrow{E} --field) boundary conditions. We found that the 2D TBA CC mode calculations were 125-150 times faster than an FDTD calculation for the same two-defect PCS. Notwithstanding this efficiency, the appropriateness of either TBA was found to depend on the geometry of the structure and the mode(s), i.e. whether or not the mode has a large normal or tangential component.

Análise comparativa dos métodos da ISO 13790 e sua adequabilidade na estimativa das necessidades de energia para aquecimento e arrefecimento e da temperatura do ar interior

Tese de mestrado integrado em Engenharia da Energia e do Ambiente, apresentada à Universidade de Lisboa, através da Faculdade de Ciências, 2016

Benchmarking numerical models of brittle thrust wedges

We report quantitative results from three brittle thrust wedge experiments, comparing numerical results directly with each other and with corresponding analogue results. We first test whether the participating codes reproduce predictions from analytical critical taper theory. Eleven codes pass the stable wedge test, showing negligible internal deformation and maintaining the initial surface slope upon horizontal translation over a frictional interface. Eight codes participated in the unstable wedge test that examines the evolution of a wedge by thrust formation from a subcritical state to the critical taper geometry. The critical taper is recovered, but the models show two deformation modes characterised by either mainly forward dipping thrusts or a series of thrust pop-ups. We speculate that the two modes are caused by differences in effective basal boundary friction related to different algorithms for modelling boundary friction. The third experiment examines stacking of forward thrusts that are translated upward along a backward thrust. The results of the seven codes that run this experiment show variability in deformation style, number of thrusts, thrust dip angles and surface slope. Overall, our experiments show that numerical models run with different numerical techniques can successfully simulate laboratory brittle thrust wedge models at the cm-scale. In more detail, however, we find that it is challenging to reproduce sandbox-type setups numerically, because of frictional boundary conditions and velocity discontinuities. We recommend that future numerical-analogue comparisons use simple boundary conditions and that the numerical Earth Science community defines a plasticity test to resolve the variability in model shear zones.

Analysis of analogue models by helical X-ray computed tomography

The aim of analogue model experiments in geology is to simulate structures in nature under specific imposed boundary conditions using materials whose rheological properties are similar to those of rocks in nature. In the late 1980s, X-ray computed tomography (CT) was first applied to the analysis of such models. In early studies only a limited number of cross-sectional slices could be recorded because of the time involved in CT data acquisition, the long cooling periods for the X-ray source and computational capacity. Technological improvements presently allow an almost unlimited number of closely spaced serial cross-sections to be acquired and calculated. Computer visualization software allows a full 3D analysis of every recorded stage. Such analyses are especially valuable when trying to understand complex geological structures, commonly with lateral changes in 3D geometry. Periodic acquisition of volumetric data sets in the course of the experiment makes it possible to carry out a 4D analysis of the model, i.e. 3D analysis through time. Examples are shown of 4D analysis of analogue models that tested the influence of lateral rheological changes on the structures obtained in contractional and extensional settings.